Problems Current and Resistance JH Suggested Problems 2 An isolated conducting sphere has a 10 cm radius One wire carries a current of 1000 002 0 A into it Another wire carries a current of 1000 000 0 A out of it How long would it take for the sphere to increase in potential by 1000 ID: 269198
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Slide1
CH26.Problems
Current
and
Resistance
JHSlide2Slide3Slide4Slide5Slide6Slide7Slide8Slide9Slide10Slide11Slide12Slide13
Suggested ProblemsSlide14
2. An isolated conducting sphere has a 10 cm radius. One wire carries a current of 1.000 002 0 A into it. Another wire carries a current of 1.000 000 0 A out of it. How long would it take for the sphere to increase in potential by 1000 V?
Answer:
5.56x10
-
3
s = 5.56
ms.Slide15
8. A small but measurable current of
1.2
x
10
-10 A exists in a copper wire whose diameter is 2.5 mm. The number of charge carriers per unit volume is
8.49
x
10
28
m
-
3
. Assuming the current is uniform, calculate the (a) current density and (b) electron drift speed.
Answer:
(a)
2.4
x
10
-
5
A/m
2
= 24
u
A
/m
2
; (b)
1.8
x
10-15 m/s. Slide16
16. Copper and aluminum are being considered for a high-voltage transmission line that must carry a current of 60.0 A. The resistance per unit length is to be 0.150
Ω
/km
. The
densities of copper and aluminum are 8960 and 2600 kg/m3, respectively. Compute (a) the magnitude J of the current density and (b) the mass per unit length
λ
for a copper cable and (c) J and (d)
λ
for an aluminum cable.
Answer:
(a)
5.33
x
10
5
A/m
2
; (b) 1.01 kg/m ; (c)
3.27
x
10
5
A/m
2
; (d) 0.477 kg/m.
Then, realistically $/m is importantSlide17
21. A common flashlight bulb is rated at 0.30 A and 2.9 V (the values of the current and voltage under operating conditions). If the resistance of the tungsten bulb filament at room temperature (20°C) is 1.1
Ω
, what is the temperature of the filament when the bulb is on?
Answer: 1.8 °C. Slide18
25. A wire with a resistance of 6.0
Ω
is drawn out through a die so that its new length is three times its original length. Find the resistance of the longer wire, assuming that the resistivity and density of the material are unchanged.
Answer: 54 Ω.Slide19
28. Figure 26-26 gives the electric potential V(
x
) along a copper wire carrying uniform current, from a point of higher potential
Vs
= 12.0 μV at x = 0 to a point of zero potential at
x
s
= 3.00 m. The wire has a radius of 2.00
mm.What
is the current in the wire?
Answer:
3.0
x
10
-
3
A = 3.0 mA.
Slide20
46. A copper wire of cross-sectional area
2.00
x
10
-6 m2 and length 4.00 m has a current of 2.00 A uniformly distributed across that area. (a) What is the magnitude of the electric field along the wire? (b) How much electrical energy is transferred to thermal energy in 30 min?
Answer:
(a)
1.69
x
10
-
2
V/m ; (b) 243 J.Slide21
47. A heating element is made by maintaining a potential difference of 75.0 V across the length of a
Nichrome
wire that has a
2.60
x10-6
m
2
cross section.
Nichrome
has a resistivity of
5.00
x
10
-
7
Ω.m
. (a) If the element dissipates 5000W, what is its length? (b) If 100 V is used to obtain the same dissipation rate, what should the length be?
Answer:
(a) 5.85 m ; (b) 10.4 m.